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arXiv:1512.00801 · Physical Review A

Vibration-induced field fluctuations in a superconducting magnet

J. Britton, Justin Bohnet, Brian C. Sawyer, Hermann Uys, Michael J. Biercuk, J. J. Bollinger

Published Jun 27, 2016• 20 citations
arXivHTMLPDF

Abstract

Superconducting magnets enable precise control of nuclear and electron spins, and are used in experiments that explore biological and condensed-matter systems, and fundamental atomic particles. In high-precision applications, a common view is that slow $(<1\phantom{\rule{4.pt}{0ex}}\mathrm{Hz})$ drift of the homogeneous magnetic-field limits control and measurement precision. We report on previously undocumented higher-frequency field noise (10--200 Hz) that limits the coherence time of $^{9}\text{Be}^{+}$ electron-spin qubits in the $4.46\ensuremath{-}\mathrm{T}$ field of a superconducting magnet. We measure a spin-echo ${T}_{2}$ coherence time of $\ensuremath{\sim}6\phantom{\rule{0.28em}{0ex}}\text{ms}$ for the $^{9}\text{Be}^{+}$ electron-spin resonance at $124\phantom{\rule{0.28em}{0ex}}\text{GHz}$, limited by part-per-billion fractional fluctuations in the magnet's homogeneous field. Vibration isolation of the magnet improved ${T}_{2}$ to $\ensuremath{\sim}50$ ms.

DOI
10.1103/physreva.93.062511

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Superconducting magnets enable precise control of nuclear and electron spins, and are used in experiments that explore biological and condensed-matter systems, and fundamental atomic particles. In high-precision applications, a common view is that slow (<1Hz)(<1\phantom{\rule{4.pt}{0ex}}\mathrm{Hz})(<1Hz) drift of the homogeneous magnetic-field limits control and measurement precision. We report on previously undocumented higher-frequency field noise (10--200 Hz) that limits the coherence time of 9Be+^{9}\text{Be}^{+}9Be+ electron-spin qubits in the 4.46\ensuremath−T4.46\ensuremath{-}\mathrm{T}4.46\ensuremath−T field of a superconducting magnet. We measure a spin-echo T2{T}_{2}T2​ coherence time of \ensuremath∼6ms\ensuremath{\sim}6\phantom{\rule{0.28em}{0ex}}\text{ms}\ensuremath∼6ms for the 9Be+^{9}\text{Be}^{+}9Be+ electron-spin resonance at 124GHz124\phantom{\rule{0.28em}{0ex}}\text{GHz}124GHz, limited by part-per-billion fractional fluctuations in the magnet's homogeneous field. Vibration isolation of the magnet improved T2{T}_{2}T2​ to \ensuremath∼50\ensuremath{\sim}50\ensuremath∼50 ms.
In this work, we study a series of tunable flux qubits inductively coupled to a coplanar waveguide resonator fabricated on a sapphire substrate. Each qubit includes an asymmetric superconducting quantum interference device, which is controlled by the application of an external magnetic field and acts as a tunable Josephson junction. The tunability of the qubits is typically $\ifmmode\pm\else\textpm\fi{}3.5\phantom{\rule{0.2em}{0ex}}\mathrm{GHz}$ around their central gap frequency. The measured relaxation times are limited by dielectric losses in the substrate and can attain ${T}_{1}\ensuremath{\sim}8\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{s}$. The echo dephasing times are limited by flux noise even at optimal points and reach ${T}_{2E}\ensuremath{\sim}4\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{s}$, almost an order of magnitude longer than state of the art.
Magnetic sensors are typically much more sensitive to oscillating (AC) magnetic fields than static (DC) fields, due to the presence of more noise at lower frequency, typically scaling with a 1/f1/f1/f dependence. For quantum magnetometers, this characteristic noise is reflected in the ensemble dephasing time T2∗T_2^*T2∗​, the relevant sensing time for a DC field, being much lower than the spin coherence time T2T_2T2​, which determines the sensitivity to AC fields. Here, we demonstrate measurement of DC magnetic fields using a physically rotating ensemble of nitrogen-vacancy centres at a precision limited by the electron spin coherence time, T2T_2T2​. We rotate the host diamond with a period comparable to T2T_2T2​, such that the angle between the NV axis and the magnetic field to be detected changes as a function of time, upconverting the static magnetic field to an oscillating field in the physically rotating frame. Using spin-echo interferometry, we observe an order of magnitude improvement in DC magnetometer response compared to a conventional Ramsey experiments. Enhancements to our scheme could realise DC sensitivities equivalent to demonstrated AC magnetic field sensitivities with NV centres.
We have developed two configurations of an echo interferometer that rely on standing-wave excitation of a laser-cooled sample of rubidium atoms. Both configurations can be used to measure acceleration aaa along the axis of excitation. For a two-pulse configuration, the signal from the interferometer is modulated at the recoil frequency and exhibits a sinusoidal frequency chirp as a function of pulse spacing. In comparison, for a three-pulse stimulated-echo configuration, the signal is observed without recoil modulation and exhibits a modulation at a single frequency as a function of pulse spacing. The three-pulse configuration is less sensitive to effects of vibrations and magnetic field curvature, leading to a longer experimental time scale. For both configurations of the atom interferometer (AI), we show that a measurement of acceleration with a statistical precision of 0.5% can be realized by analyzing the shape of the echo envelope that has a temporal duration of a few microseconds. Using the two-pulse AI, we obtain measurements of acceleration that are statistically precise to 6 parts per million (ppm) on a 25 ms time scale. In comparison, using the three-pulse AI, we obtain measurements of acceleration that are statistically precise to 0.4 ppm on a time scale of 50 ms. A further statistical enhancement is achieved by analyzing the data across the echo envelope so that the statistical error is reduced to 75 parts per billion (ppb). The inhomogeneous field of a magnetized vacuum chamber limited the experimental time scale and resulted in prominent systematic effects. Extended time scales and improved signal-to-noise ratio observed in recent echo experiments using a nonmagnetic vacuum chamber suggest that echo techniques are suitable for a high-precision measurement of gravitational acceleration ggg. We discuss methods for reducing systematic effects and improving the signal-to-noise ratio. Simulations of both AI configurations with a time scale of 300 ms suggest that an optimized experiment with improved vibration isolation and atoms selected in the mF=0{m}_{F}=0mF​=0 state can result in measurements of ggg statistically precise to 0.3 ppb for the two-pulse AI and 0.6 ppb for the three-pulse AI.
Precision measurements based on optically detected nuclear magnetic resonance offer exquisite sensitivity to absolute shifts in spin transition frequencies, with potential applications in fundamental physics experiments and inertial sensing. We investigate 13C nuclear spins in diamond as a candidate system for solid-state implementations, which hold the promise for high-fidelity readout of large numbers of coherent nuclear spins in millitesla or lower magnetic fields. We demonstrate a technique that allows for both optical polarization and readout of large ensembles of ~10^{16} polarized nuclear spins. Our method takes advantage of state-selective Landau-Zener transitions under microwave frequency sweeping, which bidirectionally transfer spin polarization between Nitrogen-Vacancy (NV) electron spins and remote 13C nuclear spins. Using natural isotopic abundance diamonds with nitrogen densities of ~0.5-10 ppm, we perform optically-detected 13C Ramsey spectroscopy and realize a nuclear-spin-dependent fluorescence contrast exceeding 0.5% peak-to-peak. We observe nuclear spin dephasing times T2*~2 ms that only modestly improve with homonuclear dipolar decoupling, indicating that they are limited by the longitudinal spin relaxation of nearby NV electron spins. We study the magnetic field dependence of the optical readout and find comparable contrast and dephasing times for magnetic fields in the range 8-20 mT. Our method can be interpreted as a type of repetitive readout, where each NV center optically reads out the spin state of ~10^2 nuclei before nuclear spins depolarize.
The microscopic description of 1/f magnetic flux noise in superconducting circuits has remained an open question for several decades despite extensive experimental and theoretical investigation. Recent progress in superconducting devices for quantum information has highlighted the need to mitigate sources of qubit decoherence, driving a renewed interest in understanding the underlying noise mechanism(s). Though a consensus has emerged attributing flux noise to surface spins, their identity and interaction mechanisms remain unclear, prompting further study. Here, we apply weak in-plane magnetic fields to a capacitively shunted flux qubit (where the Zeeman splitting of surface spins lies below the device temperature) and study the flux-noise-limited qubit dephasing, revealing previously unexplored trends that may shed light on the dynamics behind the emergent 1/f noise. Notably, we observe an enhancement (suppression) of the spin-echo (Ramsey) pure-dephasing time in fields up to B=100 G. With direct noise spectroscopy, we further observe a transition from a 1/f to approximately Lorentzian frequency dependence below 10 Hz and a reduction of the noise above 1 MHz with increasing magnetic field. We suggest that these trends are qualitatively consistent with an increase of spin cluster sizes with magnetic field. These results should help to inform a complete microscopic theory of 1/f flux noise in superconducting circuits.
We report on the measurement of atomic spin coherence near the surface of a superconducting niobium wire. As compared to normal conducting metal surfaces, the atomic spin coherence is maintained for time periods beyond the Johnson noise limit. The result provides experimental evidence that magnetic near-field noise near the superconductor is strongly suppressed. Such long atomic spin coherence times near superconductors open the way towards the development of coherently coupled cold atom/solid state hybrid quantum systems with potential applications in quantum information processing and precision force sensing.